Question

Three point masses are located in the xy plane as follows: a 1-kg mass is at the origin i.e., at (0,0), a second 1-kg mass is at x = 4m on the x axis, i.e., at (4,0), and a 2-kg mass is at the point x = 2m, by = 2m, i.e., at (2,2). Find both the x and y center of mass.

Answer 1

r= ( 2 , 1) m

Step-by-step explanation:

The important concept of center of mass is where all external forces can be applied,

`x_(cm)`= 1 /M ∑
`x_(i) m_(i)`

y_{cm} = 1 /M ∑ y_{i} m_{i}

Where x, y is the coordinate of each mass,
`m_(i)` is the mass of each point and M is the total mass of the body

Let's apply these expressions to our exercise

M = 1 + 1 +2

M = 4 kg

x_{cm} = 1/4 (1 0 + 1 4 +2 2)

x_{cm} = 2m

y_{cm} = 1/4 (1 0 + 1 0 + 2 2)

y_{cm} = 1m

coordinates of the center of mass

r= ( 2 , 1) m